8-part documentary on the Romanov family, which governed for three centuries and became linked to other European families by marriage, https://youtube.com/watch?v=USUA_1WVM8I
In 1887, their grandfather, Czar Alexander the third had Lenin's brother put up against a wall and shot. How unfortunate for the czar who signed that death warrant to have his son, daughter-in-law and grandchildren fall into the hands of the brother of the "nobody" he had had executed. The nobility had said that God's hand had given the royals the power and authority to rule Russia, but God's hand seemed not to have been much of a match to the bullet of Bolshevik soldiers.
To be fair, Vladimir's brother was only hanged because he himself had just tried to "sign the death warrant" of the tsar by tossing a bomb into his carriage...
Letting the children live would give you the problem of a vengeful (and rightful) heir in ~10 years' time. Exterminating the Romanovs completely would seem to be a pragmatic choice, given the real power of the Tsar's legend.
It's not clear that life imprisonment would have turned out very well for the Romanovs, given the lives of other political prisoners under the Soviet system; and simply freeing them would allow them to join their family members in Europe, garner support and prepare for an invasion.
Murdering innocent people is frequently pragmatic, if you're a government. That doesn't make it any less monstrous.
"Hey, at least we murdered them somewhat quickly instead of tormenting them in brutal prisons for the rest of their lives!" isn't much a defense either.
>When we began to undress the bodies, we discovered something on the daughters and on Alexandra Fyodorovna. I do not remember exactly what she had on, the same as was on the daughters or simply things that had been sewed on. But the daughters had on bodices almost entirely of diamonds and other precious stones. Those were not only places for valuables but protective armor at the same time. That is why neither bullets nor bayonets got results.